A244498 Number of magic labelings of the nodes of the 4 X 4 grid graph with magic sum n.

1, 36, 446, 3172, 15891, 62408, 204828, 585672, 1501269, 3521452, 7674810, 15723500, 30556903, 56739216, 101252408, 174482832, 291507177, 473741364, 751024438, 1164218484, 1768415099, 2636848984, 3865629780, 5579414360, 7938153405, 11145058236, 15455946546, 21190138876, 28743091407

Offset

0,2

Comments

The graph has 16 nodes and 24 edges.

The node labels are nonnegative integers, and the sum along any of the 4 rows or 4 columns is n.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: (1 + 26*x + 131*x^2 + 212*x^3 + 131*x^4 + 26*x^5 + x^6) / ((1 - x)^10).

From Colin Barker, Jan 11 2017: (Start)

a(n) = (7560 + 34164*n + 67044*n^2 + 75190*n^3 + 53382*n^4 + 25095*n^5 + 7896*n^6 + 1620*n^7 + 198*n^8 + 11*n^9)) / 7560.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>9.

(End)

Prog

(PARI) Vec((1 + 26*x + 131*x^2 + 212*x^3 + 131*x^4 + 26*x^5 + x^6) / ((1 - x)^10) + O(x^40)) \\ Colin Barker, Jan 11 2017

Crossrefs

Sequence in context: A222781 A281403 A256149 * A110693 A104671 A323549

Adjacent sequences: A244495 A244496 A244497 * A244499 A244500 A244501

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 07 2014

Status

approved